Research On Construction Of Qc-ldpc Codes Based On Matrix Extension

Quasi-Cyclic Low-Density Parity-Check codes are one of the major research topics in the information and communication field. The special structure of Quasi-cyclic codes makes it possible to use a simple encoding method and a small size of required memory, while maintaining good performance close to the Shannon-limit when iteratively decoded.This paper focuses on the simulations of optimized constructions of QC-LDPC codes. The main works are summarized as follows:1. LDPC encoding and decoding principles, as well as Tanner graph presentation of LDPC codes are introduced. The affect of girth on LDPC codes are systematically summarized, and the research and application situation of QC-LDPC codes are given.2. The special structure of QC-LDPC codes and the construction method of circulant permutation matrix based shortened array codes are represented. Simulation results show that shortening the array codes to increase the girth can lead to good performance over an additive white Gaussian noise channel.3. Based on the Chinese Remainder Theorem, we can extend the code length of a shortened array code without reducing its girth and even design a QC-LDPC code with a prescribed girth easily. Simulation results show that the constructed QC-LDPC codes can show better performance with the iterative decoding. Codes constructed with this method have flexible design code rates and code lengths.